Diagonal Electronic-Structure Hamiltonians via Multi-Basis Decomposition
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Solution Overview
Problem
Simulating electronic structure Hamiltonians is highly complex due to the exponential scaling of required resources as a function of system size, making it challenging to efficiently model and simulate large, complex quantum systems using classical processors.
Innovation Solution
Decompose the electronic structure Hamiltonian into a sum of sub-Hamiltonians, each expressed in a different basis, allowing for efficient simulation using known techniques, and implement Trotter steps with unitary operators on quantum hardware.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If the electronic structure Hamiltonian is simulated using a single basis on a quantum computer, then the simulation can be performed with a straightforward quantum circuit, but the computational resources scale exponentially with system size
Solution Approach 1:
The electronic structure Hamiltonian is decomposed into a sum of sub-Hamiltonians, each expressed in a different basis. This segmentation allows the simulation to be performed using multiple simpler quantum circuits rather than one complex circuit, reducing the exponential scaling of computational resources with system size while maintaining simulation accuracy.
2Device complexity
If the Hamiltonian is decomposed into multiple sub-Hamiltonians in different bases, then the computational cost is reduced, but the complexity of the decomposition process increases
Solution Approach 1:
The decomposition of the Hamiltonian into sub-Hamiltonians in different bases is performed as a preliminary classical computation step before quantum simulation. This preliminary action prepares the Hamiltonian in a form that reduces quantum computational resources while the classical computer handles the decomposition complexity.
3Productivity
If a compact representation of the Hamiltonian is obtained, then the simulation efficiency is improved, but the precision may be compromised
Solution Approach 1:
The Hamiltonian is represented in multiple different bases, each providing a different parameterization of the same physical system. By summing sub-Hamiltonians from multiple bases, the method achieves a compact representation that maintains simulation precision while improving efficiency, as each basis captures different aspects of the electronic structure.
Data Source
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AI summary
Methods, systems and apparatus for simulating a physical system described by an electronic structure Hamiltonian expressed in an orthonormal basis. In one aspect, a method includes decomposing the electronic structure Hamiltonian into a sum of sub-Hamiltonians, wherein each sub-Hamiltonian in the sum of sub-Hamiltonians is expressed in one of multiple bases; simulating evolution of the physical system using the decomposed electronic structure Hamiltonian; and using the simulated evolution of the physical system using the decomposed electronic structure Hamiltonian to determine properties of the physical system.